3A/3B Mathematics Specialist Imaginary and complex numbers

Notes

complex number: i= square root of -1

The conjugate of a complex number
If z=a+bi, then z=a-bi is the conjugate of z

Equal complex numbers
When two complex numbers are equal, then:
Re(w)= Re(z) and Im(w)= Im(z)
Thus if a-3i= 5+bi then a=5
and b=-3

Examples

1. z= a+bi
Real part: Re(z)=a
Imaginary part: Im(z)= b

2. z= 4+5i
Re(z)=4
Im(z)= 5

Conjugates
1. z= 2+3i, then conjugate of z is 2-3i
2. z= -3-4i, then the conjugate of z is -3+4i
3. z= 5-7i, then the conjugate of z is 5+7i

References

Unit 3B Specialist book

Contributors

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This page has been edited 2 times. The last modification was made by
- glenprideaux on Aug 1, 2009 7:57 am